




"Genetic Codes as Codes: Towards a Theoretical Basis for Bioinformatics"
Abstract: Bioinformatics has developed primarily as a discipline within mathematics and computer science devoted to organizing and analyzing large biological databases. However, biology has much to offer to a synthetic discipline of bioinformatics that draws upon and respects the mutual contributions of biology, mathematics and computer science. In particular, biology has two major theoretical foundations, both evolutionary: namely, phylogenetic systematics and population genetics, that can serve as a cornerstone of a theoretical foundation of bioinformatics along with traditional empirically driven, pattern searching forms of classical bioinformatics. In this reconception of bioinformatics... learn more...
Key words: Evolutionary Bioinformatics; Genetic Codes; Huffman Codes (Fractals and Power Laws), Gray Codes, Hamming Codes, Baudot Codes, Commafree Codes, Commaless Codes, and Overlapping Codes; codon usage; GatlinGrantham Hypotheses; Shannon's Information Theory and ChaitinKomogorov Algorithmic Complexity and Compressibility; Algebraic Coding Theory; Klein4 groups. 



"Structural Bioinformatics: Valuing Voronoi Visualization"
Abstract: Allometry and fractals have captured the imagination of mathematical biologists as well as amateurs because both apply across ten orders of magnitude of biological phenomena and structures from the molecular to the ecological level. Voronoi polygons and polyhedra are less well known to both audiences, but scale equally well. Furthermore, Voronoi polygons and polyhedra are associated with additional mathematical methods that allow deeper insight into a variety of biological phenomena such as growth, diffusion, division, packing, docking of ligands, strength of materials, molecular folding, foraging behavior, predator avoidance, and crowding as well as to their utility in making measurements, modeling interactions, relationship of two and threedimensional tomographic structures, and visualization per se. By employing Voronoi polygons and polyhedra in mathematical biology education, we will illustrate the five fold approach of curricular reform in mathematics: (1) analytical (theorem/proof), (2) numerical, (3) symbolic, (4) visual/graphical, and (5) applied to relevant scientific and social problems. While various approaches to constructing Voronoi polygons and polyhedra, Delaunay triangulations, and minimal spanning trees may be formally isomorphic from a mathematical or computer science perspective, different techniques are much better than others in helping students relate a causal mechanical and material model of their biological phenomena of interest, simulating phenomena realistically, or in making appropriate measurements. Multiple methods for constructing Voronoi polygons and polyhedra, Delaunay triangulations, and minimal spanning trees will be applied to epithelial cell boundaries, fish boundaries on sandy lake bottoms, dragonfly wing veination, crosssections of leaves, fiddler crab flocking behavior, drug design, packing of side chains in polypeptides, bird territories, and forest canopies to illustrate their commonalities and differences? Finally, statistical analyses of Voronoi polygons and Lmosaics will be compared to determine whether nearest neighbor or longrange interactions better apply to a given set of biological data.
Key words: Computational geometry, Voronoi polygons and polyhedra, Delaunay triangulations, minimal spanning trees, convex hulls, perpendicular bisectors, coordinate geometry, Voronoi fractals, simplex, alpha shapes, structural bioinformatics




"Phylogenetic Trees: Reclassifying Life, Retelling Time; Topo, Chrono, and Patrocladistics"
Abstract: Bioinformatics is the science of deriving evolutionary inferences from molecular data. Many powerful computer tools exist for conducting bioinformatic analyses, but proper interpretation of these tools' output requires a solid grasp of evolutionary principles. Particularly crucial is the ability to understand the graphs that represent the genealogy of relationships called phylogenetic trees. In this talk, we will introduce some basic phylogenetic concepts using simple treebuilding exercises: ultrametric trees, additive trees, enumerating trees. A discussion of split decomposition will highlight the nature of trees as testable evolutionary hypotheses rather than as definitive answers. Several technical concepts that are extraordinary helpful ... learn more...
Key words: Phylogenetic Systematics, Combinatorial explosions, tree topologies, ultrametric trees, additive trees, parsimony, split indices, Multiple sequence alignments, moving window averages, dot plots, gap penalties, PAM matrices 



"Systems Biology: Graph Theoretic Tools for Analyzing Metabolonomic Relationships"
Deletion Mapping Of Genetic "Fine Structure”: Supplementing Ad Hoc Problem Solving Approaches With Algorithms And Heuristics (pdf)




"Ten Equations that Changed Biology and that Should Change Biology Education"
Abstract: Mathematics has played exceptionally important roles throughout the history of biology. In this century, at least five Nobel Prizes in Physiology and Medicine involve direct contributions from mathematics. These mathematical contributions include (1) reworking complete trees of life with sequence alignment and phylogenetic tree algorithms as well as the assembly of huge genomes such as we saw in the release of the human genome a few years ago, (2) invention of three dimensional imaging that has transformed medical diagnosis through computer assisted tomography and magnetic resonance imaging, (3) development of epidemiological models of the spread of bacterial and viral infections, etc. More biology students take Calculus than any other single constituency. Too frequently, both biology and mathematics textbook authors have unappreciated... learn more...

Organized by:
Department of Mathematics and Statistics, Thammasat University, THAILAND
Funded by:
The Development Program for the Postgraduate Studies
in Mathematical Science: An Educational and Research Consortium
led by Mahidol University, with Thammasat University
and King Mongkut's Institute of Technology North Bangkok.
Materials development funded by:
The National Science Foundation, The Howard Hughes Medical Institute
and EOTPACI (Education, Outreach and Training
Partnership for Advanced Computer Infrastructure)
